Singular Values of Some Modular Functions *
نویسنده
چکیده
. We denote by A1(N) and A0(N) the modular function fields with respect to Γ1(N) and Γ0(N) respectively. Let E be a set of triples of integers a = [a1, a2, a3] with the properties 0 < ai ≤ N/2 and ai 6= aj for i 6= j. For an element τ of complex upper half plane H, we denote by Lτ the lattice in C generated by 1 and τ . Let ℘(z;Lτ ) be the Weierstrass ℘-function relative to the lattice Lτ . For a ∈ E, consider a function Wa(τ) on H defined by Wa(τ) = ℘(a1/N ; τ)− ℘(a3/N ; τ) ℘(a2/N ; τ)− ℘(a3/N ; τ) . This function is a modular function with respect to Γ1(N), referred in Chapter 18, §6 of Lang [6]. He pointed out that it is interesting to investigate its ∗2000 Mathematics Subject Classification 11F03,11G15
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